Question

$5,000 is deposited today into a bank account. The account earns 7.1% per annum compounded half yearly for the first 6 years, then 4.2% per annum compounded quarterly thereafter. Assuming no further deposits or withdrawals are made, (a) Calculate the account balance six months from today. (b) Calculate the account balance 6 years from today. (c) Calculate the account balance 6.5 years from today. (d) Calculate the account balance 10 years from today.

Answer 1

(a)	Account balance six months from today	=	Amount invested	*	Future value of 1
		=	$ 5,000.00	*	1.0355
		=	$ 5,177.50
	Working:
	Future value of 1	=	(1+0.0355)^1		Where,
		=	1.0355		i	7.1%/2	=	0.0355
					n		=	1
(b)	Account balance 6 years from today	=	Amount invested	*	Future value of 1
		=	$ 5,000.00	*	1.519852
		=	$ 7,599.26
	Working:
	Future value of 1	=	(1+0.0355)^12		Where,
		=	1.5198518		i	7.1%/2	=	0.0355
					n	6*2	=	12
(c)	Account balance 6.5 years from today	=	Amount invested	*	Future value of 1
		=	$ 7,599.26	*	1.02111
		=	$ 7,759.68
	Working:
	Future value of 1	=	(1+0.0105)^2		Where,
		=	1.0211103		i	4.2%/4	=	0.0105
					n		=	2
(d)	Account balance 6.5 years from today	=	Amount invested	*	Future value of 1
		=	$ 7,599.26	*	1.181901
		=	$ 8,981.57
	Working:
	Future value of 1	=	(1+0.0105)^16		Where,
		=	1.181901		i	4.2%/4	=	0.0105
					n	4*4	=	16